In the case of atomic ensembles, entanglement between particles is routinely detected and characterized through criteria based on low moments of collective spin observables [1]}, [2]}, [3]}, [4]}, [5]}. Moreover, bipartite entanglement has also been demonstrated between spatially separated atomic ensembles [6]}, [7]}, [8]}, [9]}. In these systems, however, entanglement quantification has so far been limited to theoretical investigations [10]}, [11]}, [12]}, [13]}, or to experiments with spinless bosons in optical lattices that assumed superselection rule or purity of the state [14]}, [15]}, i.e.   highly idealised situations.
